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Zbl 1213.53019
Vaš{\'\i}k, Petr
Transformations of semiholonomic 2- and 3-jets and semiholonomic prolongation of connections.
(English)
[J] Proc. Est. Acad. Sci. 59, No. 4, 375-380 (2010). ISSN 1736-6046

The natural transformations of semiholonomic jet functors $\overline J^{r}$ defined on the categories $\cal Mf_{m} \times \cal Mf$ and $\cal{FM}_{m,n}$ are described. Up to order three, exact coordinate formulae are known, for general order several related results are reminded. An application of semiholonomic jet transformations to prolongations of general connections is also shown. This work consists of the following parts: introduction; foundations; jets on the category $\cal Mf_{m} \times \cal Mf$; jet on the category $\cal{FM}_{m,n}$; prolongation of connections.
MSC 2000:
*53B05 Linear and affine connections
58A20 Jets

Keywords: jet; natural transformation; connection; Ehresmann prolongation

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